Neonates in intensive care require continuous monitoring. Current measurement devices are limited for long-term use due to the fragility of newborn skin and the interference of wires with medical care and parental interactions. Camera-based vital sign monitoring has the potential to address these limitations and has become of considerable interest in recent years due to the absence of physical contact between the recording equipment and the neonates, as well as the introduction of low-cost devices. We present a novel system to capture vital signs while offering clinical insights beyond current technologies using a single RGB-D camera. Heart rate and oxygen saturation were measured using colour and infrared signals with mean average errors (MAE) of 7.69 bpm and 3.37%, respectively. Using the depth signals, an MAE of 4.83 breaths per minute was achieved for respiratory rate. Tidal volume measurements were obtained with a MAE of 0.61 mL. Flow-volume loops can also be calculated from camera data, which have applications in respiratory disease diagnosis. Our system demonstrates promising capabilities for neonatal monitoring, augmenting current clinical recording techniques to potentially improve outcomes for neonates.